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6.5 Worksheet Exercise 6.5.3: Counting bit strings. How many 10-bit strings are there subject to each of the following restrictions? (a) No restrictions. 2. (b) The string starts with 001. (c) The string starts with 001 or 10. (d) The first two bits are the same as the last two bits. 6. (e) The string has exactly six O's. to ta Cl0, 6)dmon bne eousums 2a salbaxa (f) The string has exactly six O's and the first bit is 1. (g) There is exactly one 1 in the first half and exactly three 1's in the second half. (5,3) Exercise 6.5.4: Counting strings of letters. woh How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets? (a) The alphabet {a, b} ך1 (1'ב (b) The alphabet {a, b, c} (Lכ(ו Page 2 of 4 Exercise 6.5.1: Mapping permutations to subsets. e Consider a function f that maps 5-permutations from the set S = (1, ..., 20} to 5-subsets from S. The function takes a 5-permutation and creates an unordered set whose elements are the five numbers included in the 6.5 Worksheet permutation. (a) What is the value of f on input (12, 1, 3, 15, 9)? (b) Is (12, 3, 12, 4, 19) a 5-permutation? Why or why not?. e 6.7.1: Cour Yes because ny different pas then wons? Parens gth is 6 and the tockes (c) How many permutations are mapped onto the subset {12, 3, 13, 4, 19}? Pand Length is 67 Exercise 6.5.2: Permutations and combinations from a set of letters. Define the set S = {a, b, c, d, e, f, g}. (a) Give an example of a 4-permutation from the set S. is 5. %3D (Pis'qio) (b) Give an example of a 4-subset from the set S. Exer A 5-r () e0nd vhasxo bne tori tot orb mlgnoyoGxo eloedT {pigialin} Halto (c) How many subsets of S have exactly four elements? inicio onie e exsced Com EXGL ih (d) How many subsets of S have either three or four elements? (p)19buspe p ck iL 3. Page 1 of 4

6.5 Worksheet Exercise 6.5.3: Counting bit strings. How many 10-bit strings are there subject to each of the following restrictions? (a) No restrictions. 2. (b) The string starts with 001. (c) The string starts with 001 or 10. (d) The first two bits are the same as the last two bits. 6. (e) The string has exactly six O's. to ta Cl0, 6)dmon bne eousums 2a salbaxa (f) The string has exactly six O's and the first bit is 1. (g) There is exactly one 1 in the first half and exactly three 1's in the second half. (5,3) Exercise 6.5.4: Counting strings of letters. woh How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets? (a) The alphabet {a, b} ך1 (1'ב (b) The alphabet {a, b, c} (Lכ(ו Page 2 of 4 Exercise 6.5.1: Mapping permutations to subsets. e Consider a function f that maps 5-permutations from the set S = (1, ..., 20} to 5-subsets from S. The function takes a 5-permutation and creates an unordered set whose elements are the five numbers included in the 6.5 Worksheet permutation. (a) What is the value of f on input (12, 1, 3, 15, 9)? (b) Is (12, 3, 12, 4, 19) a 5-permutation? Why or why not?. e 6.7.1: Cour Yes because ny different pas then wons? Parens gth is 6 and the tockes (c) How many permutations are mapped onto the subset {12, 3, 13, 4, 19}? Pand Length is 67 Exercise 6.5.2: Permutations and combinations from a set of letters. Define the set S = {a, b, c, d, e, f, g}. (a) Give an example of a 4-permutation from the set S. is 5. %3D (Pis'qio) (b) Give an example of a 4-subset from the set S. Exer A 5-r () e0nd vhasxo bne tori tot orb mlgnoyoGxo eloedT {pigialin} Halto (c) How many subsets of S have exactly four elements? inicio onie e exsced Com EXGL ih (d) How many subsets of S have either three or four elements? (p)19buspe p ck iL 3. Page 1 of 4

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 7E
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6.5 Worksheet Exercise 6.5.3: Counting bit strings. How many 10-bit strings are there subject to each of the following restrictions? (a) No restrictions. 2. (b) The string starts with 001. (c) The string starts with 001 or 10. (d) The first two bits are the same as the last two bits. 6. (e) The string has exactly six O's. to ta Cl0, 6)dmon bne eousums 2a salbaxa (f) The string has exactly six O's and the first bit is 1. (g) There is exactly one 1 in the first half and exactly three 1's in the second half. (5,3) Exercise 6.5.4: Counting strings of letters. woh How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets? (a) The alphabet {a, b} ך1 (1'ב (b) The alphabet {a, b, c} (Lכ(ו Page 2 of 4
Transcribed Image Text:6.5 Worksheet Exercise 6.5.3: Counting bit strings. How many 10-bit strings are there subject to each of the following restrictions? (a) No restrictions. 2. (b) The string starts with 001. (c) The string starts with 001 or 10. (d) The first two bits are the same as the last two bits. 6. (e) The string has exactly six O's. to ta Cl0, 6)dmon bne eousums 2a salbaxa (f) The string has exactly six O's and the first bit is 1. (g) There is exactly one 1 in the first half and exactly three 1's in the second half. (5,3) Exercise 6.5.4: Counting strings of letters. woh How many different strings of length 12 containing exactly five a's can be chosen over the following alphabets? (a) The alphabet {a, b} ך1 (1'ב (b) The alphabet {a, b, c} (Lכ(ו Page 2 of 4
Exercise 6.5.1: Mapping permutations to subsets. e Consider a function f that maps 5-permutations from the set S = (1, ..., 20} to 5-subsets from S. The function takes a 5-permutation and creates an unordered set whose elements are the five numbers included in the 6.5 Worksheet permutation. (a) What is the value of f on input (12, 1, 3, 15, 9)? (b) Is (12, 3, 12, 4, 19) a 5-permutation? Why or why not?. e 6.7.1: Cour Yes because ny different pas then wons? Parens gth is 6 and the tockes (c) How many permutations are mapped onto the subset {12, 3, 13, 4, 19}? Pand Length is 67 Exercise 6.5.2: Permutations and combinations from a set of letters. Define the set S = {a, b, c, d, e, f, g}. (a) Give an example of a 4-permutation from the set S. is 5. %3D (Pis'qio) (b) Give an example of a 4-subset from the set S. Exer A 5-r () e0nd vhasxo bne tori tot orb mlgnoyoGxo eloedT {pigialin} Halto (c) How many subsets of S have exactly four elements? inicio onie e exsced Com EXGL ih (d) How many subsets of S have either three or four elements? (p)19buspe p ck iL 3. Page 1 of 4
Transcribed Image Text:Exercise 6.5.1: Mapping permutations to subsets. e Consider a function f that maps 5-permutations from the set S = (1, ..., 20} to 5-subsets from S. The function takes a 5-permutation and creates an unordered set whose elements are the five numbers included in the 6.5 Worksheet permutation. (a) What is the value of f on input (12, 1, 3, 15, 9)? (b) Is (12, 3, 12, 4, 19) a 5-permutation? Why or why not?. e 6.7.1: Cour Yes because ny different pas then wons? Parens gth is 6 and the tockes (c) How many permutations are mapped onto the subset {12, 3, 13, 4, 19}? Pand Length is 67 Exercise 6.5.2: Permutations and combinations from a set of letters. Define the set S = {a, b, c, d, e, f, g}. (a) Give an example of a 4-permutation from the set S. is 5. %3D (Pis'qio) (b) Give an example of a 4-subset from the set S. Exer A 5-r () e0nd vhasxo bne tori tot orb mlgnoyoGxo eloedT {pigialin} Halto (c) How many subsets of S have exactly four elements? inicio onie e exsced Com EXGL ih (d) How many subsets of S have either three or four elements? (p)19buspe p ck iL 3. Page 1 of 4
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